Point Proportional Along a Curve Constraint

Point Proportional Along a Curve Constraint

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Point_Proportional_Constraint 

A point proportion t along a curve is defined variously for different types of curves as follows:

  • For a Line segment AB, it defines the point (1-t)A + tB
  • For a Circle it defines the point on the circle which subtends angle t at the center.
  • For a Locus or envelope, it defines the point at parameter value t.
  • For general Cartesian functions, it defines the x value of the point on the function.
  • For Polar functions, it defines the point on the function which subtends angle t.
  • For general Parametric functions, it defines the point at parameter value t.
  • For an Ellipse of the form X2/a2 + Y2/b2 =1 it defines the point (a cos(t), b sin(t)).
  • For a Parabola of the form Y=X2/4a it defines the point (2at, at2)
  • For a Hyperbola of the form X2/a2 - Y2/b2 =1 it defines the point (a/cos(t), (b sin(t))/cos(t)).
  1. Select ebd_Ebd124  a point and one of the curves mentioned above.
  2. Click the Point Proportional icon ebd_Ebd125  from the Constrain toolbox, or select Point Proportional from the Constrain menu.
  3. Enter the parameter or quantity (symbolic or real) in the data entry box.

For example, in the following diagram, D is defined proportion t along AB, and E is defined proportion t along BC. The curve is the locus of F as t varies between 0 and 1.

point_proportional_01 

In the following example, the curve is the locus of the point (x,x2). Tangents are created at points with parameter values x0 and x1 on this curve.

point_proportional_02